Biorthogonal Frequency Division Multiple Access Cellular System with Angle Division Reuse Scheme

In conventional OFDMA cellular systems, mobile stations (MSs) suffer from large ICI in fully loaded cellular environments with full cell frequency reuse, especially at the cell-edge. The fundamental cause is that the signals from serving Base Station (BS) and interference BSs, are modulated by same exponential bases, at same subcarrier. In this paper, a generalized low-complexity fractional Fourier transform (FrFT) based biorthogonal frequency division multiple access (B-OFDMA) cellular system with multiple angle division reuse scheme (MADR) scheme for inter-cell interference (ICI) cancellation is proposed. FrFT angle is regarded as a kind of time-frequency combination resource (TFCR), and it can be optimally allocated to each BS of the cellular system, based on simplified minimal base correlation coefficient (MBCC) criteria, which confirms the inner-cell mutual orthogonality between modulating bases at different subcarriers, and inter-cell mutual approximate orthogonality between modulating bases at same subcarriers. Therefore, at the receiver, ICI can be dramatically suppressed by MMSE equalization and correlative detection in respective optimal FrFT domain. Extensive system simulations are conducted for various practical scenarios to demonstrate the superior performance of the proposed FrFT MADR scheme in bit error rate (BER) and system throughput, especially for cell-edge MSs, compared with conventional OFDMA cellular with different ICI cancellation schemes and scheduling schemes.     

三维物场多重分数傅里叶变换全息图光电再现实验研究

对基于多重分数傅里叶变换(FrFT)的三维(3D)物场计算全息图进行光电再现实验研究.根据分数阶与衍射距离的关系,对不同物面分别设置不同的分数阶,分别计算得到各层物面在全息面的复振幅并进行叠加,对其进行编码分别得到分数傅里叶变换振幅型全息图和相息图.同时在计算3D物场的全息图时,在物波面加入不同的随机相位因子,得到3D...     

A Novel OFDMA Cellular System Based on Multiple FrFT Angles Reuse Scheme

In conventional Orthogonal Frequency Division Multiple Access (OFDMA) cellular systems, the fundamental cause of inter-cell interference (ICI) is that the signals from serving Base Station (BS) and interference BSs, are modulated by same exponential bases, at same subcarrier. In this letter, an effective OFDMA cellular mobile system based on multiple fractional Fourier transform (FrFT) angle reuse scheme is proposed. In this system, FrFT angle is regarded as new resource, which can be optimally allocated to each BS of cellular system. Because chirp bases, generated by different FrFT with optimally allocated angle, are mutually approximately orthogonal at same subcarrier, ICI can be perfectly suppressed. Both theory and simulations show the essential advantages over conventional OFDMA cellular systems for ICI suppression and bit error rate.     

A Novel Multi-carrier Order Division Multi-access Communication System Based on TDCS with Fractional Fourier Transform Scheme

In this paper, we propose a novel fractional Fourier transform (FrFT) based multi-carrier order division multi-access communication system, in which each user is uniquely identified by an FrFT order. Transform domain communication system (TDCS) with FrFT scheme is also proposed to synthesize the wide-band baseband waveforms in all FrFT domains with different users’ FrFT orders, which enhances the interference avoidance capability of this system under most of interference. Therefore, multiple independent data streams can be transmitted by using FrFT–OFDM in the same time and different FrFT domains. However, chirp bases, as the new kind of carriers with different modulated rates, are merely mutually approximately orthogonal. There is a problem of energy leakage between multiple chirp carriers, which possibly causes the multiple chirp carriers inter-shielding to influence the FrFT–OFDM demodulation performance. An efficient allocation algorithm of multiple chirp carriers by presetting the carrier parameters is proposed to solve this problem. Based on MC-CDMA, a variable bit rate system structure is proposed for TDCS with FrFT scheme under different channel environments. In order to simplify the process of modulation and demodulation of TDCS with FrFT scheme, a whole new cyclic shift key modulation mode in FrFT domain is also proposed. Both theories and simulations confirm strictly the validity of the proposed system.     

Analysis of Chirp as windowing function through fractional Fourier transform

This article presents a new mathematical model for obtaining the fractional Fourier transform (FrFT) of Chirp function. FrFT is a parameterised transform having an adjustable transform parameter which makes it more flexible and superior over ordinary FT in several applications. It is an important tool used in signal processing for spectral analysis. The closed-form expression derived for FrFT of finite duration Chirp establishes the dependence of FrFT of Chirp on the order of FrFT and the Chirp parameter. The mathematical model obtained shows that the Chirp function can be used as an adjustable window function in the fractional Fourier domain. The main-lobe width, side-lobe level and side-lobe fall-off rate of a Chirp window can be controlled by changing the adjustable transform parameter to different values. For some particular values of fractional angle, Chirp can give better spectral parameters than the existing window functions. By varying the order of FrFT, the variations in spectral parameters of the Chirp window are obtained and studied. The performance of the Chirp window in fractional domain is also compared with some of the existing windows.     

Closed-Form Analytical Expression of Fractional Order Differentiation in Fractional Fourier Transform Domain

In this paper, a closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional order calculus. The reported work is a generalization of the differentiation property to fractional (noninteger or real) orders in the FrFT domain. The proposed closed-form analytical expression is derived in terms of the well-known confluent hypergeometric function. An efficient computation method has also been derived for the proposed algorithm in the discrete-time domain, utilizing the principles of the discrete fractional Fourier transform algorithm. An application example of a low-pass finite impulse response (FIR) fractional order differentiator in the FrFT domain has also been investigated to show the practicality of the proposed method in signal processing applications.     

基于频域遮隔及分数阶相关的反辐射导弹检测技术

该文提出一种基于频域遮隔及分数阶相关来检测反辐射导弹(ARM)的新方法。该方法利用雷达回波的频域(Fourier变换)数据,根据尖锋作遮隔处理后,直接运用基于分数阶Fourier变换(FrFT)和Fourier逆变换的分数阶相关方法,通过一维搜索来检测ARM。由于该方法利用了现有的Fourier数据,且分数阶Fourier变换可以通过Fourier变换实现,无需多通道相位补偿和二维搜索,故计算量小。仿真结果表明,该方法能够在ARM信噪比低达#61485;10dB,ARM与载机回波功率比为#61485;27dB的情况下,准确地检测出ARM,从而实现ARM发射的早期告警。     

The discrete fractional Fourier transform based on the DFT matrix

We introduce a new discrete fractional Fourier transform (DFrFT) based on only the DFT matrix and its powers. Eigenvectors of the DFT matrix are obtained in a simple-yet-elegant and straightforward manner. We show that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the continuous FrFT. By appropriately combining existing commuting matrices we obtain a new commuting matrix which performs better. We show the validity of the proposed algorithms by computer simulations comparing DFrFT points and continuous FrFT samples for various signals.     

基于变形FrFT和线性同余的光学图像加密算法

基于双随机相位编码光学图像加密系统,利用线性同余发生器（LCG）生成随机相位,结合变形分数傅里叶变换（AFrFT）,提出了一种改进的光学图像加密方法。方法的特点是：LCG函数的4个参数都可作为密钥;相比常规FrFT,变形FrFT的分数阶数目多1倍;算法密钥的数量从2重增加到8重,并且还有2个辅助密钥,大大提高了加密系统...     

Sampling and Reconstruction of Sparse Signals in Fractional Fourier Domain

Sampling theory for continuous time signals which have a bandlimited representation in fractional Fourier transform (FrFT) domain-a transformation which generalizes the conventional Fourier transform-has blossomed in the recent past. The mechanistic principles behind Shannon's sampling theorem for fractional bandlimited (or fractional Fourier bandlimited) signals are the same as for the Fourier domain case i.e. sampling (and reconstruction) in FrFT domain can be seen as an orthogonal projection of a signal onto a subspace of fractional bandlimited signals. As neat as this extension of Shannon's framework is, it inherits the same fundamental limitation that is prevalent in the Fourier regime-what happens if the signals have singularities in the time domain (or the signal has a nonbandlimited spectrum)? In this paper, we propose a uniform sampling and reconstruction scheme for a class of signals which are nonbandlimited in FrFT sense. Specifically, we assume that samples of a smoothed version of a periodic stream of Diracs (which is sparse in time-domain) are accessible. In its parametric form, this signal has a finite number of degrees of freedom per unit time. Based on the representation of this signal in FrFT domain, we derive conditions under which exact recovery of parameters of the signal is possible. Knowledge of these parameters leads to exact reconstruction of the original signal.     

Fractional Fourier transform of the Gaussian and fractional domain signal support

The fractional Fourier transform (FrFT) provides an important extension to conventional Fourier theory for the analysis and synthesis of linear chirp signals. It is a parameterised transform which can be used to provide extremely compact representations. The representation is maximally compressed when the transform parameter, /spl alpha/, is matched to the chirp rate of the input signal. Existing proofs are extended to demonstrate that the fractional Fourier transform of the Gaussian function also has Gaussian support. Furthermore, expressions are developed which allow calculation of the spread of the signal representation for a Gaussian windowed linear chirp signal in any fractional domain. Both continuous and discrete cases are considered. The fractional domains exhibiting minimum and maximum support for a given signal define the limit on joint time-frequency resolution available under the FrFT. This is equated with a restatement of the uncertainty principle for linear chirp signals and the fractional Fourier domains. The calculated values for the fractional domain support are tested empirically through comparison with the discrete transform output for a synthetic signal with known parameters. It is shown that the same expressions are appropriate for predicting the support of the ordinary Fourier transform of a Gaussian windowed linear chirp signal.     

基于变换域和时域联合处理的雷达同频干扰抑制方法

针对舰艇编队情况下线性调频脉冲体制雷达间同频干扰的问题,该文提出一种分数阶傅里叶域滤波处理与时域反异步处理相结合的干扰抑制方法。通过分数阶傅里叶域自适应滤波对与目标回波信号调频率不同的干扰信号做抑制处理,同时根据分数阶傅里叶变换的可逆性,逆变换到时域后采用相邻周期反异步方法进一步消除与目标回波信号调频率相同或相近的同频干扰。仿真试验表明,该方法相对传统方法能够有效抑制与目标回波信号调频率不同的同频干扰,同时对于在时域与目标回波信号完全重合或部分重合的干扰信号也有较好的抑制效果,干扰抑制处理增益达到29 dB以上。该方法为提高同型雷达编队组网能力提供了设计参考。     

Propagation properties of controllable dark-hollow beams through fractional Fourier transform systems

Based on the definition of fractional Fourier transform(FrFT) in the cylindrical coordinate system,the propagation properties of a controllable dark-hollow beam(CDHB) are investigated in detail.An analytical formula is derived for the FrFT of a CDHB.By using the derived formula,the properties of a CDHB in the FrFT plane are illustrated numerically.The results show that the properties of the intensity of the beam in the FrFT are closely related to not only the fractional order but also initial beam parameter,beam order and the lens focal length of the optical system for performing FrFT.The derived formula provides an effective and convenient way for analyzing and calculating the FrFT of a CDHB.     

A blind watermarking algorithm based on fractional Fourier transform and visual cryptography

This paper presents a robust copyright protection scheme based on fractional Fourier transform (FrFT) and visual cryptography (VC). Unlike the traditional schemes, in our scheme, the original image is not modified by embedding the watermark into the original image. We use the visual secret sharing scheme to construct two shares, namely, master share and ownership share. Features of the original image are extracted using SVD, and are used to generate the master share. Ownership share is generated with the help of secret image (watermark) and the master share, using VC technique. The two shares separately give no information about the secret image, but for ownership identification, the secret image can be revealed by stacking the master share and the ownership share. In order to achieve the robustness and security, the properties of VC, FrFT and SVD are used in our scheme. The experimental results show that the proposed scheme is strong enough to resist various signal processing operations.     

不对称分数傅里叶变换计算全息

提出了不对称分数傅里叶变换计算全息,并给出了相应算法。将输入图像信息分别经过x,y不同方向实施不同级次的分数傅里叶变换,采用迂回位相法对其分数域谱编码,绘出计算全息图。再现时需用两个特定的柱面透镜才能再现出所记录的图像信息,利用其再现方式的特殊性可制成一种安全认证系统,计算机上模拟演示结果表明,利用该方法进行安全认证,在防伪力度提高的同时,实际应用也更为方便,具有很高的安全性。     

微弱LFM信号的FrFT检测能力分析

基于分数阶傅里叶变换（FrFT）检测线性调频（LFM）信号广泛应用于雷达、通信、声呐和电子战领域,但缺乏对检测灵敏度的定量分析。为此,研究了FrFT对微弱LFM信号的检测能力。根据FrFT思想和二元假设检验理论,推导了检测概率和虚警概率的数学表达式。由于表达式是关于LFM信号频谱的函数,因此区分快变信号和慢变信号对LFM的频谱进行了合理近似。基于接收机工作特性曲线分析了FrFT检测LFM信号的灵敏度。仿真比较了FrFT与传统傅里叶变换（FT）对微弱LFM信号的检测能力,结果表明FrFT对LFM信号的检测灵敏度和信号累积能力均优于FT。     

An Efficient VLSI Architecture for Computation of Discrete Fractional Fourier Transform

Since decades, the fractional Fourier transform (FrFT) has attracted researchers from various domains such as signal and image processing applications. These applications have been essentially demanding the requirement of low computational complexity of FrFT. In this paper, FrFT is simplified to reduce the complexity, and further an efficient CORDIC-based architecture for computing discrete fractional Fourier transform (DFrFT) is proposed which brings down the computational complexity and hardware requirements and provides the flexibility to change the user defined fractional angles to compute DFrFT on-the-fly. Architectural design and working method of proposed architecture along with its constituent blocks are discussed. The hardware complexity and throughput of the proposed architecture are illustrated as well. Finally, the architecture of DFrFT of the order sixteen is implemented using Verilog HDL and synthesized targeting an FPGA device ”XLV5LX110T”. The hardware simulation is performed for functional verification, which is compared with the MATLAB simulation results. Further, the physical implementation result of the proposed design shows that the design can be operated at a maximum frequency of 154 MHz with the latency of 63-clock cycles.     

一种改进的基于FrFT的SAR运动目标检测与成像方法

针对传统的基于FrFT的SAR地面运动目标检测方法的不足,该文结合分数阶Fourier域滤波、重排谱图以及CLEAN思想,提出了一种改进的方法。该方法能够以较高精度估计目标的多普勒起始频率和中心频率,并能分辨在时频平面位于同一直线的多个目标。最后给出了FrFT数值计算结果与有量纲的多普勒参数之间的转换公式。仿真结果表明了该方法的有效性。     

分数傅里叶变换计算全息图

提出了分数傅里叶变换计算全息图 (FRTCGH)。采用分数傅里叶变换的快速算法和罗曼Ⅲ型迂回位相编码方法设计并制作了一个物体不同分数阶的分数傅里叶变换计算全息图 ,用罗曼Ⅰ型分数傅里叶变换光学系统再现原物体 ,得到了物体清晰的像。分析了FRTCGH和再现图像随分数阶变化的规律 ,讨论了分数傅里叶变换计算全息图与菲涅耳计算全息图之间的关系。     

Iterative Interpolation for Parameter Estimation of LFM Signal Based on Fractional Fourier Transform

This study introduces two iterative interpolation algorithms for the parameter estimation of linear frequency modulation (LFM) signal using fractional Fourier transform (FrFT). The estimated parameter of an LFM signal can be obtained by locating the peak of the periodogram in the FrFT domain. Two interpolation algorithms were proposed to improve the accuracy of parameter estimation by employing the FrFT coefficients relative to the true parameters and applying interpolation algorithms iteratively to refine the parameter estimation approach. The proposed algorithms can utilize more information from FrFT results, thereby achieving improvements in either accuracy or efficiency. Moreover, the simulation results revealed the validity and advantage of the proposed approach.